As described in [1]}, one can learn to predict the noise present in the data with a network \(\varepsilon _\theta \)  and sample from \(p_\theta (x_{t-1}|x_t)\)  using the following formula :
\(x_{t-1} = \dfrac{x_t - \frac{1 - \alpha _t}{\sqrt{1- \bar{\alpha }_t}}\varepsilon _\theta (x_t, t)}{\sqrt{\bar{\alpha }_t}} + \sigma _t \varepsilon \,,\) 
